- #1
daiviko
- 6
- 0
I'm attempting to teach myself topology from a textbook. I'm on the first chapter and came into some trouble with some of the set theory.
Here is what the textbook says.
We make a distinction between the object a, which is an elemant of a set A, and the one-element set {a}, which is a subset of A. To illustrate if A is the set {a,b,c}, then the following statements are all correct.
•a is an element of A
•{a} is a subset of A
•{a} is an element of P(A) where P(A) i the power set of A meaning that P(A) is the set of all subsets of A.
However according to the textbook the following statements are not true
•{a} is a member of A
•a is a subset of A
If the set {a}, simply contains a what is the difference between saying a is an "element" of A and a is a "subset" of A? If an object is an element of some set isn't it also a subset of that set? I also am having trouble understanding the idea of a power set. If P(A) is the set of all subsets then doesn't P(A)=A?
Here is what the textbook says.
We make a distinction between the object a, which is an elemant of a set A, and the one-element set {a}, which is a subset of A. To illustrate if A is the set {a,b,c}, then the following statements are all correct.
•a is an element of A
•{a} is a subset of A
•{a} is an element of P(A) where P(A) i the power set of A meaning that P(A) is the set of all subsets of A.
However according to the textbook the following statements are not true
•{a} is a member of A
•a is a subset of A
If the set {a}, simply contains a what is the difference between saying a is an "element" of A and a is a "subset" of A? If an object is an element of some set isn't it also a subset of that set? I also am having trouble understanding the idea of a power set. If P(A) is the set of all subsets then doesn't P(A)=A?